Juan José Aguilar

Stereo vision for 3D measurement : accuracy analysis, calibration and industrial applications

This paper evaluates the accuracy of different camera calibration and measurement methods used in 3D stereo vision with CCD cameras. These methods are evaluated by means of several precision tests, determining their error limits under specified conditions of operation. To check the precision of such systems, a CMM and some calibration objects, such as grids, plates, spheres, etc. are used. Two practical applications are described: a cost-effective system for the measurement of free-form surfaces, able to generate CAD models and measuring programs for CMMs. The system aims to reduce some difficulties associated with stereo vision and to speed up the traditional digitizing process. The other application involves car frame measurement. A new automatic measuring system has been developed, allowing contactless car frame measurement through two rotating CCD cameras.

A one-step intrinsic and extrinsic calibration method for laser line scanner operation in coordinate measuring machines

A technique for intrinsic and extrinsic calibration of laser line scanners, also called laser triangulation sensors (LTSs), for integration in a coordinate measuring machine (CMM) is presented in this paper. Setting out from the modeling of a commercial LTS for use in a CMM and the algorithms implemented for image capture and processing, with the use of a gauge object, a one-step calibration procedure has been developed to obtain both intrinsic parameters?laser plane, CCD sensor and camera geometry?and extrinsic parameters which relate the LTSs reference system to the CMMs reference system, integrating both mathematical models. This method performs both calibrations in a single step, thus avoiding the digitalization of a reference sphere in order to obtain the extrinsic parameters, or optimization procedures subsequent to LTS calibration. The results obtained in accuracy and repeatability tests performed on gauge geometric primitives attest to the viability of this technique for the integration of LTSs in CMMs.

3D Geometrical Inspection of Complex Geometry Parts Using a Novel Laser Triangulation Sensor and a Robot

This article discusses different non contact 3D measuring strategies and presents a model for measuring complex geometry parts, manipulated through a robot arm, using a novel vision system consisting of a laser triangulation sensor and a motorized linear stage. First, the geometric model incorporating an automatic simple module for long term stability improvement will be outlined in the article. The new method used in the automatic module allows the sensor set up, including the motorized linear stage, for the scanning avoiding external measurement devices. In the measurement model the robot is just a positioning of parts with high repeatability. Its position and orientation data are not used for the measurement and therefore it is not directly “coupled” as an active component in the model. The function of the robot is to present the various surfaces of the workpiece along the measurement range of the vision system, which is responsible for the measurement. Thus, the whole system is not affected by the robot own errors following a trajectory, except those due to the lack of static repeatability. For the indirect link between the vision system and the robot, the original model developed needs only one first piece measuring as a “zero” or master piece, known by its accurate measurement using, for example, a Coordinate Measurement Machine. The strategy proposed presents a different approach to traditional laser triangulation systems on board the robot in order to improve the measurement accuracy, and several important cues for self-recalibration are explored using only a master piece. Experimental results are also presented to demonstrate the technique and the final 3D measurement accuracy.

Modelling and Calibration Technique of Laser Triangulation Sensors for Integration in Robot Arms and Articulated Arm Coordinate Measuring Machines

A technique for intrinsic and extrinsic calibration of a laser triangulation sensor (LTS) integrated in an articulated arm coordinate measuring machine (AACMM) is presented in this paper. After applying a novel approach to the AACMM kinematic parameter identification problem, by means of a single calibration gauge object, a one-step calibration method to obtain both intrinsic—laser plane, CCD sensor and camera geometry—and extrinsic parameters related to the AACMM main frame has been developed. This allows the integration of LTS and AACMM mathematical models without the need of additional optimization methods after the prior sensor calibration, usually done in a coordinate measuring machine (CMM) before the assembly of the sensor in the arm. The experimental tests results for accuracy and repeatability show the suitable performance of this technique, resulting in a reliable, quick and friendly calibration method for the AACMM final user. The presented method is also valid for sensor integration in robot arms and CMMs.

Towards an effective identification strategy in volumetric error compensation of machine tools

The influence of technical parameters for volumetric error compensation in large-volume machine tools (MTs) is presented in this paper. The techniques presented are based on characterization models using nonlinear optimization procedures. The parameters presented allow for the characterization of different errors in the MT studied and depend on the kinematics and geometry of the system, regardless of the optimization methodology. The kinematics is affected by the MT errors on the number and type of axes and movements. To relate the coordinates of the tool to the coordinates of a laser tracker, a kinematic model of the MT that includes the measurement system must be defined. Kinematic models can be realized by using homogeneous transformation matrices or independent rotation and translation arrays according to the type of machine. Chebyshev, simple or Legendre polynomial regression functions can be used to characterize the geometric errors of the MT and are presented and compared. The distribution of measurement points, mesh or cloud, and optimization constraints of polynomial regressions are factors that also affect volumetric error compensation. Therefore, these parameters were studied and presented as well. In addition to the parameters discussed above, another parameter that affects the accuracy of data capture is the measurement noise. To improve the measurement accuracy, multilateration techniques need to be applied. Each of the aforementioned parameters has been studied by using a synthetic test generated by a parametric synthetic data generator. The selected parameters constitute a package of optimization improvement regardless of the optimization methodology, which have improved the nonlinear optimization from 60–70% to 98%.

A self-centering active probing technique for kinematic parameter identification and verification of articulated arm coordinate measuring machines

A crucial task in the procedure of identifying the parameters of a kinematic model of an articulated arm coordinate measuring machine (AACMM) or robot arm is the process of capturing data. In this paper a capturing data method is analyzed using a self-centering active probe, which drastically reduces the capture time and the required number of positions of the gauge as compared to the usual standard and manufacturer methods. The mathematical models of the self-centering active probe and AACMM are explained, as well as the mathematical model that links the AACMM global reference system to the probe reference system. We present a self-calibration method that will allow us to determine a homogeneous transformation matrix that relates the probes reference system to the AACMM last reference system from the probing of a single sphere. In addition, a comparison between a self-centering passive probe and self-centering active probe is carried out to show the advantages of the latter in the procedures of kinematic parameter identification and verification of the AACMM.

Modelling and calibration of parallel mechanisms using linear optical sensors and a coordinate measuring machine

This paper presents a new procedure for the modelling and calibration of a parallel mechanism by using linear optical sensors and a coordinate measuring machine. Three standard spheres, fixed to the moving platform, were measured by means of a coordinate measuring machine. Additionally, a control algorithm was developed to store sensor readings in each analysed position. These readings and the kinematic model allow us to obtain the calculated sphere coordinates. The use of high-accuracy linear optical sensors allows us to correct actuator backlash, thereby increasing the mechanism accuracy. The developed method defines an objective function that compares the measured and calculated coordinates of the three-sphere centres in order to obtain the identified model parameters that minimize this difference. This procedure combines both inverse and forward kinematics, and solves the nonlinear system loop of the kinematic model inside a second loop that optimizes the geometric parameters of the model. Numerical optimization techniques based on Levenberg–Marquardt algorithm are used to solve both optimization loops. Results show that the platform position and orientation errors are improved by more than one order of magnitude.

Analysis of Tsai calibration method using two- and three-dimensional calibration objects

Camera calibration is a fundamental process for both photogrammetric and computer vision. Since the arrival of the direct linear transformation method and its later revisions, new methods have been developed by several authors, such as: Tsai, Heikkilä and Zhang. Most of these have been based on the pinhole model, including distortion correction. Some of these methods, such as Tsai method, allow the use of two different techniques for determining calibration parameters: a non-coplanar calibration technique using three-dimensional (3D) calibration objects, and a coplanar technique that uses two-dimensional (2D) calibration objects. The calibration performed by observing a 3D calibration object has good accuracy, and produces very efficient results; however, the calibration object must be accurate enough and requires an elaborate configuration. In contrast, the use of 2D calibration objects yields less accurate results, is much more flexible, and does not require complex calibration objects that are costly to produce. This article compares these two different calibration procedures from the perspective of stereo measurement. Particular attention was focused on the accuracy of the calculated camera parameters, the reconstruction error in the computer image coordinates and in the world coordinate system and advanced image-processing techniques for subpixel detection during the comparison. The purpose of this work is to establish a basis and selection criteria for choosing one of these techniques for camera calibration, according to the accuracy required in each of the many applications using photogrammetric vision: robot calibration methods, trajectory generation algorithms, articulated measuring arm calibration, and photogrammetric systems.

Design Optimization for the Measurement Accuracy Improvement of a Large Range Nanopositioning Stage

Both an accurate machine design and an adequate metrology loop definition are critical factors when precision positioning represents a key issue for the final system performance. This article discusses the error budget methodology as an advantageous technique to improve the measurement accuracy of a 2D-long range stage during its design phase. The nanopositioning platform NanoPla is here presented. Its specifications, e.g., XY-travel range of 50 mm × 50 mm and sub-micrometric accuracy; and some novel designed solutions, e.g., a three-layer and two-stage architecture are described. Once defined the prototype, an error analysis is performed to propose improvement design features. Then, the metrology loop of the system is mathematically modelled to define the propagation of the different sources. Several simplifications and design hypothesis are justified and validated, including the assumption of rigid body behavior, which is demonstrated after a finite element analysis verification. The different error sources and their estimated contributions are enumerated in order to conclude with the final error values obtained from the error budget. The measurement deviations obtained demonstrate the important influence of the working environmental conditions, the flatness error of the plane mirror reflectors and the accurate manufacture and assembly of the components forming the metrological loop. Thus, a temperature control of ±0.1 °C results in an acceptable maximum positioning error for the developed NanoPla stage, i.e., 41 nm, 36 nm and 48 nm in X-, Y- and Z-axis, respectively.

Volumetric Verification of Multiaxis Machine Tool Using Laser Tracker

This paper aims to present a method of volumetric verification in machine tools with linear and rotary axes using a laser tracker. Beyond a method for a particular machine, it presents a methodology that can be used in any machine type. Along this paper, the schema and kinematic model of a machine with three axes of movement, two linear and one rotational axes, including the measurement system and the nominal rotation matrix of the rotational axis are presented. Using this, the machine tool volumetric error is obtained and nonlinear optimization techniques are employed to improve the accuracy of the machine tool. The verification provides a mathematical, not physical, compensation, in less time than other methods of verification by means of the indirect measurement of geometric errors of the machine from the linear and rotary axes. This paper presents an extensive study about the appropriateness and drawbacks of the regression function employed depending on the types of movement of the axes of any machine. In the same way, strengths and weaknesses of measurement methods and optimization techniques depending on the space available to place the measurement system are presented. These studies provide the most appropriate strategies to verify each machine tool taking into consideration its configuration and its available work space.